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Approximating Multivariate Tempered Stable Processes

Part of: Stochastic processes

Published online by Cambridge University Press:  04 February 2016

Boris Baeumer  and
Mihály Kovács
Boris Baeumer*
Affiliation:
University of Otago
Mihály Kovács*
Affiliation:
University of Otago
*
∗ Postal address: Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin, New Zealand.
∗ Postal address: Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin, New Zealand.
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Abstract

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We give a simple method to approximate multidimensional exponentially tempered stable processes and show that the approximating process converges in the Skorokhod topology to the tempered process. The approximation is based on the generation of a random angle and a random variable with a lower-dimensional Lévy measure. We then show that if an arbitrarily small normal random variable is added, the marginal densities converge uniformly at an almost linear rate, providing a critical tool to assess the performance of existing particle tracking codes.

Keywords

Tempered stable processsimulationLévy processoperator stable processspectral measure

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 60G52: Stable processes
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 1 , March 2012 , pp. 167 - 183
Copyright
© Applied Probability Trust 

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